- #1
mrroboto
- 35
- 0
I should just give math up, I don't understand this at all. It seems like for a) the function could be squared, and other than that it doesn't make any sense.
Let V = {p element of R[x] | deg(p) <=3} be the vector space of all polynomials of degree 3 or less.
a) Explain why the derivative d/dx: V -> V is a linear function
b) Give the matrix for d2/dx2 in the basis {1,x,x^2, x^3} for V
c) Give the matrix for the third derivative d2/dx2: V->V using the same basis
d) Give the matrix for the third derivative d3/dx3: V->V using the same basis
e) Give a basis for ker(d2/dx2)
f) what is the matrix for the linear map (d/dx + 4(d3/dx)): V->V
g) Let T: R[x] ->R[x] be the function T(p(x))= integral from -2x to 2 of p(t)dt
Explain why T is an element of L(R[x])
Let V = {p element of R[x] | deg(p) <=3} be the vector space of all polynomials of degree 3 or less.
a) Explain why the derivative d/dx: V -> V is a linear function
b) Give the matrix for d2/dx2 in the basis {1,x,x^2, x^3} for V
c) Give the matrix for the third derivative d2/dx2: V->V using the same basis
d) Give the matrix for the third derivative d3/dx3: V->V using the same basis
e) Give a basis for ker(d2/dx2)
f) what is the matrix for the linear map (d/dx + 4(d3/dx)): V->V
g) Let T: R[x] ->R[x] be the function T(p(x))= integral from -2x to 2 of p(t)dt
Explain why T is an element of L(R[x])